Financial markets have successfully demanded the imposition of severe austerity on the periphery of the eurozone – Greece, Ireland and Portugal – to deal with public debt. The markets have also raised concerns about it in the United States, Britain and Japan, clamouring for austerity. Public debt seems to operate like a mask behind which lies a shadowy world of creditors to whose upkeep entire economies are mortgaged.

Can that mask be lifted? It has been in other countries, through the mechanism of a debt audit. Initiatives like this have happened in Brazil, Ecuador and elsewhere in order to untangle the web of secrecy around the debt and work out who lent what to whom, when and for what purpose. Typically, there is an expectation that some, at least, of the debt, will be found to be "illegitimate", and can therefore be repudiated.

Ecuador provides a striking example. In 2007 President Correa established a debt audit commission, which reported in 2008 that a portion of the country's debt was indeed illegitimate and had done "incalculable damage" to Ecuador's people and environment. The price of illegitimate debt subsequently collapsed in the open markets, and Ecuador got rid of it easily.

Despite predictions of economic disaster the country registered 3.7% economic growth in 2010, and the forecast is for growth in excess of 5% in 2011. The salience of the Ecuadorian example for current debates in Europe is obvious.

This is why a campaign for a Greek audit commission was launched in March with the support of civil organisations, trade unions and political parties. One of its greatest successes has been the documentary Debtocracy, which has been watched by a million people. In a country that feels humiliated and dejected, the campaign has offered a modicum of hope. Such has been its popular appeal that, in a singularly ill-judged remark, a minister denounced it for equating Greece with "Latin American banana republics".

In an example of European solidarity several bodies, including Action from Ireland, the Irish Debt and Development Coalition and the trade union Unite, are, on 4 May, launching a debt audit in Ireland. Academics with expertise in economics, finance, law and related disciplines are being commissioned to trawl through the public accounts to tackle several questions. To whom is the bank debt owed? When was it contracted? Specifically, was it before or after the government's September 2008 bank guarantee was issued? When is the debt due for repayment? How much has already been repaid, and to whom?

Meanwhile the Greek campaign is taking steps to start its own investigations. What is the legal status of debt contracted with the helpful services of Goldman Sachs that presented public borrowing as a derivative transaction? How legal is debt to finance further arms procurement in one of the most militarised countries in the world? Above all, how legitimate is the extraordinary loan of €110bn by the European Union and the International Monetary Fund that it is claimed is needed to "bail out" the country – at the price of ferocious public spending austerity? The loan did not follow the normal procedure for contracting public debt, including approval by Greece's parliament.

These preliminary investigations will establish facts to further the demand for a full democratic audit and a sovereign response to debt. What is ultimately necessary is full access to debt data, the power to examine witnesses, and even the ability to examine bank accounts. On this basis properly constituted audit commissions could make credible recommendations on debt that is illegitimate or simply unsustainable. The sovereign state could then take appropriate action, including repudiation of debt and cessation of payments.

The campaigns for debt audits will also have an important educational function to perform across Europe. People in core countries, including Germany, seem not to have yet grasped that the loans provided by the EU and the IMF are not bailing out feckless Mediterraneans and Celts. In fact they are bailing out banks that engaged in profitable and irresponsible lending throughout the 2000s. And that will be a theme of a gathering of activists in Athens on 6-8 May. Participants from across the world will trade ideas on how to tackle European public debt. After more than three years of crisis, grassroots movements are at last emerging to oppose the grip of debt, austerity and neoliberalism across Europe.